Question

if alpha and beta are the zero's of quadratic polynomial f(x) =x*x-x-2 find a polynomial who's zeros are 2 alpha +1 and 2 bita + 1 ?

Answer 1

You can factorize your given polynomial as follows:

x^2 - x - 2 = 0
=> (x + 1)(x - 2) = 0
The roots are thus x = 2, x = -1
Alpha = 2, beta = -1

Coming to the next part, (2alpha + 1) = 5, (2beta + 1) = -1

You can thus use these roots to form the following polynomial:

(x - 5)(x + 1) = 0
=> x^2 - 4x - 5 = 0